Journal of Transport Economics and Policy, Volume 47, Part 3, September 2013, pp. 349–369
Marginal Costs, Price Elasticities of Demand, and
Second-best Pricing in a Multiproduct Industry
An Application for Spanish Port Infrastructure
Ramón Núñez-Sánchez
Address for correspondence: Departamento de Economı́a, Universidad de Cantabria, Avda. Los
Castros, s/n 39005 Santander (Spain) ([email protected]).
This research has been partially funded by Ministerio de Ciencia e Innovación (Spain) grants
PSE-370000-2008-8 and PSE-370000-2009-11. I also want to express my gratitude to Soraya
Hidalgo for research assistance. I am indebted to the anonymous referees whose comments
significantly helped to improve the paper.
Abstract
This paper tries to evaluate the price-setting structure for the Spanish port authorities during the
period 1986–2005. To do this, we compare the structure of the most important port fees with those
results obtained using a second-best mechanism based on Ramsey prices. The results show that
port fees do not maximise social surplus due to the existence of heterogeneity among port
authorities. In this sense, a new regulation which would allow port authorities to set their own fees
may represent an improvement for the present mechanism.
Date of receipt of final manuscript: May 2012
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1.0 Introduction
Most of the theoretical discussions about an optimal port pricing rule focus on marginal
cost pricing which maximises the social surplus. However, actual pricing policies
normally differ from this ideal pricing structure (Strandenes and Marlow, 2000). The
implementation of this theoretical general solution is extremely difficult for the port
context, due to both the nature of the industry and the existence of different multiple
agents which interact among them.
As with other similar organisations that manage transport infrastructures (airports,
railway networks, roads), short-run marginal costs are relatively low with regards to
fixed building costs and, in this sense, cost recovery using the optimal pricing rule would
not be possible. In order to overcome this problem, economic literature gives us some
solutions to find mechanisms which allow allocative inefficiencies to be minimised. The
first solution could be to use the concept of long-run marginal cost, which is defined as
the sum of short-run marginal cost plus marginal cost of capacity increase. However,
this solution presents several drawbacks as, for example, the fact that port infrastructure
has an indivisible nature means it cannot continuously enlarge. Another theoretical
solution would be the use of a second-best pricing rule based on Ramsey prices. This
methodology has commonly been used in some network industries such as transport,
water, sewerage or postal services (Train, 1977; Youn Kim, 1995; Cuthbertson and
Dobbs, 1996; Garcia and Reynaud, 2004).
On the other hand, in most European ports, the organisation which coordinates the
use of common facilities and owns port infrastructure is called the port authority. This
type of entity is usually a public-owned institution, while port operators which control
port services (cargo handling, consignees and ancillary services) are privately owned.
Regional development, universal service or geographical cohesion are the main reasons
to justify the existence of public-owned port infrastructures. During the last decades,
however, the cost recovery or self-financing of port authorities has been an important
aim for them. In this sense, port fees (also known as port dues or port charges) have
been essential for port authorities in order to finance the building of port infrastructure.
This source of income charges different agents for the use of the general infrastructure of
a port.
This paper tries to evaluate the pricing system for the Spanish port authorities during
the period 1986–2005. To do this, we compare the structure of the different port fees
with the results obtained using a second-best mechanism based on Ramsey prices. First,
we estimate a system of equations, including a multi-product short-run cost function and
different demand functions. The estimation of demand functions for the use of port
infrastructure enables us to calculate fee elasticities of demand, which we consider a
novelty in the literature, given that we have not found previous studies which quantify
the sensibility of the demand for these services with regard to port fees. Then, we
calculate the different marginal costs for the provision of infrastructure and their
corresponding price elasticities of demand.
It is important to stress that optimal pricing within ports should be proportional to
the costs generated including three items: cargo handling; the time in port for the vessel
and cargo; and port dues and fees (Meersman et al., 2003). However, in this work we
have considered only the cost associated with the last item, due to the limitations on
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Núñez-Sánchez
data about time-related operational cost and cargo handling.1 Therefore, this research
only takes into account the monetary costs related to the providers of port infrastructure: port authorities. On the other hand, cost related to time is important as a
component of the generalised cost of the vessel or cargo. However, this concept is less
essential if ports do not suffer congestion problems. We assume that this is the case of
Spanish ports in general terms.
The paper is structured as follows. Section 2 describes the Spanish port system and
fees structure between 1986 and 2005. Section 3 describes the theoretical model. Section
4 contains the econometric specification of a multi-output variable cost function and the
demand functions. Section 5 explains the data and defines the variables used in our
analysis. Section 6 presents the results of the estimation of marginal costs and price
elasticities of demand, comparing the fee structure with those obtained through the
Ramsey pricing model. Finally, Section 7 summarises the main conclusions.
2.0 Description of the Spanish Port System (1986–2005)
2.1 An overview of the Spanish port system
The state-owned port system in Spain consists of forty-six general interest ports,
managed by twenty-seven port authorities. The public entity, Puertos del Estado (literally
State Ports, a state-owned enterprise of national ports), is responsible for coordination and
efficiency control. Spanish legislation provides the port system with the necessary instruments to improve its competitive position in an open, global market, setting up extended
self-management faculties for the port authorities (for example, investment decisions). In
order to fulfil these objectives, the main tasks of Puertos del Estado are the identification of
specific management goals, the assignment of resources and the corresponding financial
instruments, management control, the design of common information and accounting
systems, and the general planning of investments by the port authorities.
It should be emphasised that nowadays the Spanish port system is based on a selffinancing policy for port authorities and it does not receive any direct subsidies from the
national government. In this way, current and investment expenditures are covered by
current incomes, special European Union subsidies, and occasionally by external debt.
Port authorities, therefore, must obtain a volume of income such that they can
finance the running costs as well as capital expenditure, and additionally achieve a
reasonable return for investment in fixed assets.2
Within this framework and since 1992 when a new general law for ports became
effective (Law 27/1992), general interest ports are intended to correspond to the landlord
model, whereby the port authority does no more than provide the port land and infrastructure, while regulating the use of this public property. Other relevant functions are
public land use regulation, anti-trust control of port services, specialisation of facilities,
1
There are an important number of studies that deal with evaluating the productive structure of port operators. In
this way, Jara-Dı́az et al. (2005) analyse the cost structure for three different cargo-handling firms located in the
same port.
2
This return could be interpreted, from an economic point of view, as the opportunity cost, for which, in reality, the
condition imposed upon the port authorities is that the economic profits are zero.
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environmental precautions, and safety within the port space. Port services are essentially
provided by private sector operators under an authorisation or concession regime; these
include berthing services, piloting, towing, mooring and cargo handling, among others.
As the World Bank (2007) affirms, in the landlord port model, infrastructure is
leased to private operating companies and/or to industries such as refineries, tank
terminals, and chemical plants. The lease to be paid to the port authority is usually a
fixed sum per square metre per year, typically indexed using some measure of inflation.
The amount of the lease is related to the initial preparation and construction costs (for
example, land reclamation and quay wall construction). The private port operators
provide and maintain their own superstructure, including buildings (for example, offices,
sheds, warehouses, container freight stations, workshops). They also purchase and install
their own equipment on the terminal grounds (for example, dock cranes, conveyor belts)
as required by their business.
2.2 Pricing in the Spanish port system (1986–2005)3
According to Trujillo and Nombela (2000), port fees are relevant when shipping
companies or exporters/importers have to choose among different ports, although their
importance is relatively small compared to the total cost that port users must bear. In
this way, port fees on the use of infrastructure would represent between 5 and 15 per
cent of the total monetary cost, these costs being associated with cargo handling, the
most important concept of the total bill (70–90 per cent).
In general terms, incomes may be classified in three different types: those which
finance general services; those related to specific services; and finally rents, associated
with the use of public land for private firms. In Table 1 we observe the revenues’ structure of Spanish port authorities for the period 1986–2005.
Regarding the first type of income, those include services related to: signalling (lights,
buoys), commercial vessels (berths, docks), cargo, passengers, and sport vessels. It
represents 71 per cent of the total income for the period 1986–2005, income associated with
the vessel (17 per cent) and the cargo (48 per cent) being the most important. The income
associated with specific services is related to the use of cranes, storage or energy supplies.
As we see in Figure 1, this income has been decreasing in importance in recent years,
representing 7 per cent in 2005. The progressive change from a tool port model, where
superstructures used to be owned by port authorities but operated by private firms, to the
landlord port model, in which a superstructure is owned and operated by private operators,
could explain it. The rent associated to the use of public land for private firms is the second
most important source of income (27 per cent of the total income in 2005). This type of
rent has been increasing in importance in recent years, due to the nature of the landlord
port model, in which port authorities lease port infrastructure to the private sector.
There are several reasons why we only focus on the income for general services.
First, the charges that were historically associated with cargo and vessels have been the
principal source of income for ports in financing their investments in infrastructures.4
3
Other papers that study the Spanish port reform during the 1990s are Castillo-Manzano et al. (2008), González
and Trujillo (2008), and Núñez-Sánchez et al. (2011).
4
A good historical and legal approximation about the charges of port authorities in Spain can be found in Navarro
Fernández (2007).
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Núñez-Sánchez
Marginal Costs, Price Elasticities of Demand, and Second-best Pricing
Table 1
Revenues’ Structure of Spanish Port Authorities. Means for the Period 1986–2005
Thousands of constant euros 2001 ¼ 100
Percentage
Maritime signalling
Ships (berths, docks)
Cargo and passengers
Fish
Sport vessels
Other general services
110.56
3,927.16
10,977.44
488.25
161.53
440.26
0.48
17.20
48.07
2.14
0.71
1.93
General services
Cranes
Storage
Energy supplies
Other specific services
16,105.21
1,253.02
571.91
519.20
777.89
70.53
5.49
2.50
2.27
3.41
Specific services
3,122.02
13.67
Land rents
3,607.46
15.80
22,834.69
100.00
Total income
Second, in spite of the growing importance of rents associated with public land, they
cannot be considered as prices in an economic sense, given that these rents are usually
defined as a percentage of the market value of the land in which the port is located.
Therefore, in economic terms, these rents should express the opportunity cost of the
aforementioned land.
In spite of the fact that the Port Law 27/1992 allows a decentralisation process in
decision making within the Spanish port system to be initiated, the pricing policy of
Spanish ports ultimately depends on the Ministerio de Fomento (Ministry of Public
Figure 1
Revenues’ Structure of Spanish Port Authorities, 1986–2005
0.8
0.7
General
services fees
0.5
0.4
Specific
services fees
0.3
Land rents
0.2
0.1
0
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
Percentage
0.6
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Journal of Transport Economics and Policy
Volume 47, Part 3
Works and Transport), this being — after the proposal made by the State Ports and
after listening to the associations of users in the state area who were directly affected,
mainly shipping and travelling users — the organism that fixes the rates that port
authorities charge for financing investments, as well as their running costs. It has to be
emphasised that these charges are common for all twenty-seven port authorities, which
means that free competition in prices for each of the ports is not possible.
In order to award certain flexibility to the system, from the point of view of income,
the Ministry establishes minimum and maximum limits for all port authorities. In this
way, a curious paradox is produced within the port system. On the one hand, legislation
allows the ports to make their own decisions in strategic matters, with the ultimate aim
of self-financing, but, on the other hand, these are limited when it comes to freely
choosing their running costs.
In 1997, when Law 62/1997 came into effect and modifying Law 27/1992, two
important changes occurred: autonomous communities began to form part of the
administration councils within the port authorities; and there was an intensification in
freedom of port fees, giving ports the authority to fix basic tariff charges for port
services, with no further limits than their own market strategies. However, in the 3rd
Transitory Regulation of Law 62/1997, the application of this objective was proposed
for a period of three years, maintaining the intervention of the Ministry of Public Works
and Transport in the sector. In short, the new regulation in 1997 tried to increase the
degree of port autonomy, offering incentives for competition between different ports of
general interest, even though the freedom of prices was never fully implemented.
The last reform, which took place in the period between 1986 and 2005, came into
effect with Law 48/2003, in which all references to the general application for freedom of
prices for port authorities disappeared. With this new reform, the only thing that was
granted was the freedom to set prices for the previously mentioned specific services
which, as we previously mentioned, carry very little weight in relation to port funding.
With respect to general services, this new law continues to fix maximum and minimum
limits for different charges, although such flexibility is determined by the general profitability obtained by the port authorities.
3.0 Theoretical Problem
As we pointed out in the previous section, the most important fees in order to finance
the infrastructure of ports are those fees related to general services for commercial
vessels and cargo. On the other hand, the system of port fees to fund port infrastructures
is a centralised system, where the Ministry of Public Works and Transport is the
organism which ultimately decides the charges which can be made to port authorities.
Assuming, a priori, that ports are productive units with considerable economies of scale,
optimal or first-best pricing would produce economic losses, which is why the principle
of self-financing could not be carried out. The model stated below which we propose is a
model in which State Ports propose a tariff mechanism common to all second-best type
port authorities, based on a tariff system using Ramsey prices. In this way, we define the
decision problem of State Ports as the maximisation of a total surplus function, which is
defined as the sum of consumer surplus plus the profit of the port authority, subject to a
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Marginal Costs, Price Elasticities of Demand, and Second-best Pricing
Núñez-Sánchez
classical economic constraint: it has to achieve the zero-profit condition:
X
n Z Qi
n
X
Max W ¼ CS þ ¼
pi ðX Þ dX pi Qi þ
pi Q i C ð Q 1 ; . . . ; Q n Þ
Qi
0
i¼1
i¼1
ð1Þ
s:t: ¼ 0:
Defining the Lagrangean function of the constrained problem (1):
n Z Qi
X
~
‘ Q; l ¼
pi ðX Þ dX pi Qi
i¼1
þ
n
X
0
"
pi Q i C ð Q 1 ; . . . ; Q n Þ þ l
i¼1
n
X
#
pi Q i C ð Q 1 ; . . . ; Q n Þ ;
i¼1
we calculate the first order condition:
3
2
~; l
~
~
@‘ Q
@C Q
@C Q
@p
5 ¼ 0:
¼ 0 ! pi þ l4 i Q i þ p i @qi
@qi
@Qi
@Qi
Reordering the latter expression, we obtain:
~
pi MCi Q
pi
¼
l
1
;
1 þ l jeii j
ð2Þ
ð3Þ
where jeii j ¼ ðdQi =dpi Þð pi =Qi Þ is the own price elasticity of demand for good i and
1=1 þ l is called the Ramsey number, which is the function of the shadow price for the
constraint of the problem (1) also called Lagrange multiplier l 5 0. The Ramsey pricing
rule is also known as the inverse elasticity rule, since it means that outputs with relatively
inelastic demands will have greater markups. That is, the amount by which prices exceed
marginal costs, expressed as a Lerner index, is greater for outputs with less elastic demand.
We could also formulate an alternative problem of decision: the maximisation of a
function of social surplus, defined as the balanced sum of m different indirect utility
functions, subject to the fact that port authorities present zero economic profits:
m X
Max
a jV j ~
p; R j
pk
s:t:
j¼1
n
X
ð4Þ
pi Qi ¼C ðQ1 ; . . . ; Qn Þ:
i¼1
Assuming that port authorities lend their services to two different outputs, thereafter the
first-order conditions, we obtain the following Ramsey pricing rule:
3
2
~
pj MCj Q
7
6
7 je j þ e
6
pj
6
kk
jk
7
;
ð5Þ
7 ¼ 6
7
6 p MC Q
e
þ
e
~
jj
kj
k
5
4 k
pk
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Volume 47, Part 3
Journal of Transport Economics and Policy
where jekk j þ ejk and ejj þ ekj are called superelasticities. For the case of the port
authorities’ outputs (cargo and vessels), we consider both as complements, so cross-price
elasticities of demand should have negative values. In this sense, it could be the case that
the price of one output is less than its corresponding marginal cost, given that the crossprice effect is significant enough. In order to test whether the two most important fees of
port authorities to finance infrastructure are a second-best solution, we should estimate
marginal costs for cargo and vessels, and we should obtain own and cross-fee elasticities
of demand related to cargo and vessels.
4.0 Econometric Estimation
4.1 Estimation of the variable cost function and cost expenditure equations
For the estimation of the multi-product variable cost function we have chosen a
flexible functional form, the multi-product quadratic function with variables deviated
from their mean. It is based upon a second-order Taylor series expansion around the
mean values:
VCit ¼ a0 þ
m
X
r Þ þ
br ðQrit Q
r¼1
þ
n X
n
X
m X
m
X
r ÞðQsit Q
s Þ þ
brs ðQrit Q
r¼1 s¼1
n
X
jÞ
gj ðWjit W
j¼1
j ÞðWkit W
kÞ
gjk ðWjit W
j¼1 k¼1
þ
m X
n
X
r ÞðWjit W
j Þ þ Z f ðFit FÞ
rrj ðQrit Q
r¼1 j¼1
þ Zff ðFit FÞ2 þ
m
X
r Þ þ
sfr ðFit FÞðQrit Q
r¼1
þ
P
X
i¼1
þ
n
X
pi Di þ xa ðTt TÞþxaa ðTt TÞ2 þ
n
X
jÞ
rfj ðFit FÞðWjit W
j¼1
m
X
r ÞðTt TÞ
fra ðQrit Q
r¼1
j ÞðTt TÞþtf ðFit FÞðTt TÞ þ eit ;
zj ðWjit W
ð6Þ
j¼1
where VCit is the total variable cost of a port authority i in a year t, Qrit is the amount
of output r of a port authority i in a year t, Wjit is the input j price of a port authority i
in a year t, Fit is the amount of the quasi-fixed input of a port authority i in a year t, Di
is a dummy which captures the individual cost effects of port authorities, and T is a time
trend representing technical change. Given that the time trend T interacts with input and
output variables, the model allows studying non-neutral technical change, and a0 , br ,
brs , gj , gjk , rrj , Zf , Zff , sfr , rfj , pi , xa , xaa , fra , zj , tf are parameters to be estimated, m
represents the number of outputs, and n is the number of inputs. Variables with a
horizontal bar on top represent sample means.
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Núñez-Sánchez
Marginal Costs, Price Elasticities of Demand, and Second-best Pricing
We can apply Shephard’s Lemma to obtain input cost expenditure equations to be
estimated with the cost function, improving the efficiency of the parameter estimation:
Ejit ¼ Wjit
@VCit
¼ wjit Xjit
@Wjit
"
jÞ þ
¼ Wjit gj þ 2gjj ðWjit W
n
X
kÞ
gjk ðWkit W
k¼1
þ
m
X
#
r Þ þ rfj ðFit FÞ þ zj ðTt TÞ þ nit :
rrj ðQrit Q
ð7Þ
r¼1
We can also calculate port authorities’ specific marginal costs for outputs at their
corresponding mean values of outputs and prices:5
MCr ¼
m
n
X
X
@VC
r Þ þ
s Þ þ
jÞ
¼ br þ 2brr ðQr Q
brs ðQs Q
rrj ðWj W
@qr
j¼1
s 6¼ r
þ sfr ðFit FÞ þ fra ðTt TÞ:
ð8Þ
The multi-output degree of short-run scale economies, SE — also called economies of
density (Christensen and Greene, 1976) — measure short-run economies associated with
increased production, given a certain level of the quasi-fixed input (in this case, the
deposit surface). Economies of density are defined on the technology as the maximal
proportionate growth rate of outputs, as all the variable inputs are expanded proportionally, which means solving for S in FðlX; lS Q; SÞ ¼ 0, where F is the transformation
function and l is the proportion by which variable inputs increase. It can be calculated
from the cost function at a point as:
S¼
~; W
~Þ
VCðQ
:
m
X
MCr Qr
ð9Þ
r¼1
In the single output case, equation (9) reduces the ratio between average and marginal
costs. As Bottasso and Conti (2010) point out, short-run scale economies are relevant
when computed in the case of industries characterised by the presence of infrastructures
that cannot be easily modified in the short-run, like most network industries or airport
and port sectors.
4.2 Estimation of the demand functions
In order to calculate own and cross-price elasticities of cargo and vessel demand, we
estimate two different demand equations. Assuming a semi-logarithm functional form,
we indirectly obtain the values of those elasticities. The cargo demand function (Qc ) is
5
For simplicity, we omit the sub-index for port authorities (i) and year (t).
357
Volume 47, Part 3
Journal of Transport Economics and Policy
expressed as follows:
ln Qcit ¼ git þ d0 ð pcit Þ þ d1 ð psit Þ þ
p
X
ci Di þ
T
X
zt Dt þuit ;
ð10Þ
xt Dt þeit :
ð11Þ
t¼1
i¼1
and the vessel demand function (Qs ):
ln Qsit ¼ yit þ B0 ð psit Þ þ B1 ð pcit Þ þ
p
X
i¼1
ji Di þ
T
X
t¼1
The intercept term of both demands includes variables which try to capture some
different factors influencing inter-port competition among different port authorities.
Navas (2003) distinguishes three different types of factors: those related with the
geographical position; those depending on physical and infrastructural features; and finally
those associated with operating conditions. The intercept term groups the first two.
Regarding the first group, we have included one variable: the added value of the region in
which the port is located (inc), in order to capture the importance of its hinterland. Another
two variables capture physical and infrastructural features: the number of linear metres of
deep water berths of more than 4 m (draft) and the number of pieces of cargo handling
equipment6 (inf ), which includes gantry cranes, ship-shore gantries, yard cranes, and
mobile cranes.
In this way, the intercept for the cargo demand function is expressed as:
git ¼ g0 þ g1 lnðincit Þ þ g2 lnðinfit Þ;
ð12Þ
and the intercept for the vessel demand function:
yit ¼ y0 þ y1 lnðincit Þ þ y3 lnðdraftit Þ:
ð13Þ
Both demands also depend on cargo and vessel fees ( p). These variables capture the
operating conditions of the different port authorities. Other important variables related
to the operating conditions are, speed movement of cargo, safety of cargo, or the
number of regular shipping lines. Unfortunately, however, we have not found enough
information to include them in the study. For the specification of equations (10) and
(11) we have also included dummies which try to capture individual and temporal effects.
These individual demand effects of port authorities are especially important given that
they take into account some factors related to the geographical position of ports.
5.0 Data
5.1 Definition of variables for the estimation of the variable cost system
The sample consists of the twenty-six7 port authorities. Annual data comprises the
period between 1986 and 2005. Appendix 1 shows some descriptive statistics for the
6
The use of cranes as an infrastructure variable is always controversial. After testing various specifications, we
decided to add the number of cranes into a single variable. The main reason justifying such a decision is that
this article does not take into account the different types of cargo, so this variable in the cargo demand function
would be a proxy for port size. This variable has been used in other studios, as in Cullinane et al. (2002).
7
The Port Authority of Sevilla was not included in the analysis as it is the only river port and, therefore, its cost
structure responds to a quite different technology.
358
Marginal Costs, Price Elasticities of Demand, and Second-best Pricing
Núñez-Sánchez
variables used for the estimation of cost and expenditure equations. The final panel data
set consists of 520 observations. There, total variable annual costs (VC) represent the
dependent variable that includes labour expenditures (El), capital expenditures (Ek), and
intermediate consumption expenditures (Eic). Labour costs comprise the payments of
labour and Social Security expenses. Capital expenditures are calculated as total annual
provisions for amortisation and variation in provision for bad trade debts. Finally,
intermediate consumption comprises consumption (for example, office supplies, water,
electricity), and external supplies and services. The explanatory variables of the multioutput cost function for the infrastructure services of Spanish ports comprise two
outputs, three input prices and one quasi-fixed input. The output variables of ports
represent the movements of cargo (Qcargo) and vessels, measured as the aggregate gross
tonnage of vessels which entered the ports (Qgt).
Labour price (Wl) is calculated as total labour expenditure over the total number of
employees. Regarding input prices, capital price (Wk) is calculated as an index price
of public works (ICNC, ı́ndice de precios de la Confederación Nacional de la
Construcción)8 multiplied by the sum of real long-term interest rate (R), and the
depreciation rate of the port’s property and equipment (d). The depreciation rate is
calculated as the annual depreciation expenditures of each port authority over the total
assets. The following expression shows the method to calculate capital price for every
port authority, Wk ¼ ICNCðR þ dÞ.
Intermediate input price (Wic) is defined as the ratio between the sum of consumption, externally provided services, plus other expenses and annual revenue. Finally, the
existing deposit surface of every port authority (F ) has been considered as a quasi-fixed
input, given that it is not possible to enlarge a port in a continuous way.
5.2 Definition of variables for the estimation of demand equations
Appendix 1 shows some descriptive statistics for the variables used for the estimation of
demand equations (10) and (11). As dependent variables, we have used the movement of
cargo (Qcargo) and vessels, measured as the aggregate gross tonnage of vessels which
entered the ports (Qgt), respectively. Regarding the independent variables, we have defined
the cargo and vessel fees (pc and pS) for every port authority as the average income; that is,
the ratio between the annual income collected for fees related to cargo or vessel, and the
total movement of cargo or vessel. Other variables which have been considered for the
estimation were: the added value of the region in which the port is located, as proxy to
the importance of the hinterland (inc); the number of linear metres of docks with deep water
higher than 4 m (draft); and the number of pieces of cargo-handling equipment (inf ).
6.0 Results
6.1 Results for the estimation of the variable cost system and demand functions
Although it is possible to estimate separately the quadratic variable cost function and
the demand functions, it would lead to an efficiency loss. In this way, we employ a
8
This price index was collected from the National Building Confederation (Confederación Nacional de la
Construcción).
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Journal of Transport Economics and Policy
Volume 47, Part 3
full-information method by estimating the system of equations, which include the
variable cost equation, cost expenditure equations, and demand equations for cargo and
vessels.
In Table 2, we observe the estimation of the multi-product variable cost system
(equations (6) and (7)) by means of three-stage least squares (3SLS). All the variables are
expressed in deviations with respect to their means. Therefore, the first-order coefficients
relating to the outputs can be interpreted as their marginal costs evaluated at the sample
mean. As the economic theory remarks, a variable cost function must satisfy the regularity conditions: it should be non-decreasing, quasi-concave and homogeneous of degree
zero in prices of the variable inputs, and non-decreasing in outputs. These properties
have been verified in our specification, so we confirm that port authorities minimise their
variable costs. The marginal cost evaluated at the sample mean for cargo is 0.35€ per
ton, whereas marginal cost for vessels is 0.06€ per gt. Comparing these values with the
mean for cargo and vessel fees (1.34€ per ton and 0.23€ per gt), we admit that both fees
are higher than their marginal costs, so price regulation on port authorities does not
correspond to a first-best solution. On the other hand, the first-order coefficient relating
to the deposit area and considered as a quasi-fixed input is positive but not statistically
different from zero. This result is counter-intuitive in terms of the economic theory,
given that this means the marginal productivity of the total area is zero. However, this
result is very common in studies related to the technology structure of utilities.9 Two
reasons could explain this result. First, port infrastructure cannot be built in a continuous way, so it is not possible to meet present demand without the existence of overcapitalisation. Most infrastructures are built in order to meet future increasing demand.
Second, zero or negative marginal productivity could be explained as a result of some
features of the regulatory regime for Spanish ports. In this way, as we mention in Section
2.1, port authorities must obtain a volume of income such that they can finance the
running costs as well as capital expenditure, and additionally achieve a reasonable return
for investment in fixed assets. This kind of rate-of-return regulation typically distorts the
input ratios. Finally, given that a coefficient related to the trend is negative, port authorities presented a process of technological change. Meanwhile, second-order coefficients
associated with the trend say that this process becomes less important over the period
analysed. The existence of non-neutral technological change has allowed that the
demand for labour and intermediate consumption has decreased.
The estimation of the variable cost system of equations allows us to calculate individual marginal costs for every single port authority (equation (8)). Moreover, it is possible
to test the existence of increasing returns to scale for the technology structure of port
authorities (equation (9)). For the sample mean, economies of density are equal to about
2.95, thus implying that a 1 per cent proportional increase in all outputs would lead
total variable costs to rise by 0.34 per cent in the short-run.
Equations (10)–(13) define the demand functions, which depend on cargo fees, vessel
fees, the added value of the corresponding hinterland, and the equipment of the port or
the number of linear metres of quays. Other factors that can affect demand are the main
9
Some examples are Rodrı́guez-Alvarez et al. (2007) for the case of port cargo-handling firms, or Bottasso and
Conti (2009) for water and sewerage companies.
360
Núñez-Sánchez
Marginal Costs, Price Elasticities of Demand, and Second-best Pricing
Table 2
Parameter Estimates
Coefficient
Std. Error
t-Statistic
Prob.
Cost parameters
constant
Wl
Wk
Wic
Qcargo
Qgt
F
Qcargo Qcargo
Qgt Qgt
F F
Wl Wl
Wk Wk
Wic Wic
Qcargo Qgt
Qcargo F
Qgt F
Wl r
Wl Wic
Wk Wic
F Wl
F Wk
F Wic
Qcargo Wl
Qcargo Wk
Qcargo Wic
Qgt Wl
Qgt Wk
Qgt Wic
trend
trend trend
trend Qcargo
trend Qgt
trend F
trend Wl
trend Wk
trend Wic
16057242
211.582
1208153
12986795
0.348
0.063
1.401
5.7E-09
3.84E-10
1.47E-06
0.001
12341
4899983
1.21E-09
3.58E-07
1.47E-08
7.576
34.987
312517
0.00011
0.877
5.912
2.41E-06
0.030
0.375
5.82E-07
0.004
0.105
219865
24965
0.008
0.006
0.597
8.495
7825
513220
2375839
3.796
25041
326530
0.091
0.031
1.371
6.74E-09
3.55E-10
6.94E-07
7.13E-05
3703
499080
2.3E-09
9.25E-08
1.34E-08
1.177
23.411
73572
0.00001
0.046
0.567
5.39E-07
0.003
0.043
1.28E-07
0.001
0.010
64371
5085
0.005
0.003
0.096
0.698
5455
48211
6.758556
55.731
48.247
39.772
3.835
2.035
1.021
0.846
1.084
2.116
11.535
3.333
9.818
0.525
3.874
1.100
6.439
1.494
4.248
16.490
19.168
10.432
4.472
8.590
8.813
4.540
4.685
10.045
3.416
4.909
1.647
2.405
6.194
12.162
1.434
10.645
0.000
0.000
0.000
0.000
0.000
0.042
0.307
0.398
0.278
0.035
0.000
0.001
0.000
0.600
0.000
0.271
0.000
0.135
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.000
0.100
0.0162
0.000
0.000
0.152
0.000
Cargo demand parameters
constant
PC
PS
ln(inc)
ln(inf )
12.941
0.339
0.270
0.177
0.361
1.555
0.034
0.292
0.086
0.039
8.324
10.023
0.923
2.064
9.209
0.000
0.000
0.356
0.039
0.000
Vessel demand parameters
constant
PC
PS
ln(inc)
ln(draft)
11.280
0.078
1.352
0.250
0.290
1.578
0.032
0.286
0.082
0.085
7.148
2.470
4.734
3.048
3.422
0.000
0.014
0.000
0.002
0.001
Notes: R2 for VC, El, Ek, Eic, Qcargo, and Qgt are 0.95, 0.68, 0.72, 0.73, 0.96, and 0.97, respectively. Estimation of
cost function includes variable dummies for individual ports, and estimation of both demands includes variable
dummies for individual ports and temporal effects.
361
Journal of Transport Economics and Policy
Volume 47, Part 3
distance of the port with the main commercial route for vessels, or the distance among
other ports; however, the effect of these variables over the demand are controlled by the
inclusion of the individual effects for every port authority, given that those effects are
time constant. We have assumed a semi-logarithm form for the demands in order to
obtain different fee elasticities for every single port authority. We have also included
temporal effects. Table 1 shows the estimation of port infrastructure demand function
for cargo, which reveals that the coefficient associated to the cargo fee is negative and
statistically different from zero, as predicts the economic theory. On the other hand, the
coefficient related to the vessel fee is also negative but not statistically different from
zero, so we could interpret that the variation of fees related to the vessel does not affect
the port infrastructure demand function for cargo. This result could be explained due to
the relatively low value of this concept of a fee. Individual effects for every single port
authority are statistically significant, so we could admit that those individual timeconstant effects impact the demand of port infrastructure for cargo. In this sense the
location of port infrastructure would be an important factor to explain the demand of
services for cargo. Temporal effects are also statistically different from 1992. It is
important to stress that this year, a new law for ports became effective (Law 27/1992).
Finally, we observe that both the added value of the hinterland and the equipment of
the port positively affect the demand of port infrastructure for cargo.
Regarding the estimation of demand for port infrastructure for vessels, we observe
that both coefficients associated with fees are negative and statistically different from
zero, showing the complementary nature of cargo and vessels. Unlike the previous
estimation, the cross-fee effect is statistically significant, given that the variation on cargo
fees affects the demand of port infrastructure for vessels. On the other hand, both
individual time-constant effects and temporal effects are statistically significant. Other
variables which positively affect the demand of port infrastructure for vessels are the
added value of the hinterland and the number of linear metres of deep water berths of
more than 4 m.
In Table 3, the individual marginal costs for cargo and vessels at the mean and their
corresponding markups are shown. The existence of port fees (both cargo and vessel),
higher than marginal costs, is economically justified in order to cover investment costs of
these infrastructures.
Regarding individual marginal costs, differences among different port authorities are
quite significant. The highest marginal costs for cargo come from Barcelona (0.85€ per
ton) and Valencia (0.82€ per ton), whereas Bahı́a de Algeciras (0.1€ per ton) presents the
lowest value. On the other hand, the port authorities of Bilbao (0.11€ per gt) and Pasajes
(0.1€ per gt) present the highest marginal costs for vessels. The lowest marginal costs for
vessels are for Bahı́a de Algeciras (0.001€ per gt).
The estimation of marginal costs for the different outputs allows us to calculate their
markup, using also fees related to cargo and vessels. In this way, it is possible to
determine the left-hand side of equation (5).
Table 3 also presents markups for cargo and vessel fees. Since markups for cargo are
greater than zero, this suggests that cargo fees charged to customers are in excess of
marginal costs for every single port authority. The highest and lowest value for markup
related to cargo is for Marı́n y Rı́a de Pontevedra (0.89) and Castellón (0.02), respectively. Regarding the markups for vessels, we observe that there are port authorities that
362
Núñez-Sánchez
Marginal Costs, Price Elasticities of Demand, and Second-best Pricing
Table 3
Marginal Costs, Markups and Elasticities of Demand
(PC MCC)/ (PS MCS)/
PC
PS
eCC
eCS
eSS
eSC
0.252
0.463
0.252
0.430
0.540
0.608
0.354
0.321
0.152
0.666
0.262
0.308
0.322
0.317
0.441
0.339
1.024
0.453
0.516
0.605
0.018
0.046
0.039
0.107
0.050
0.040
0.090
0.082
0.062
0.007
0.072
0.141
0.084
0.086
0.035
0.055
0.007
0.010
0.098
0.119
0.088
0.232
0.195
0.535
0.253
0.199
0.451
0.411
0.310
0.034
0.359
0.709
0.420
0.433
0.174
0.274
0.037
0.052
0.489
0.596
0.058
0.107
0.058
0.099
0.124
0.140
0.081
0.074
0.035
0.153
0.060
0.071
0.074
0.073
0.102
0.078
0.236
0.104
0.119
0.139
Port Authority
MCc
MCS
Bahı́a de Algeciras
Alicante
Almerı́a-Motril
Avilés
Bahı́a de Cádiz
Barcelona
Bilbao
Cartagena
Castellón
Ceuta
Ferrol-S. Cibrao
Gijón
Huelva
A Coruña
Las Palmas
Málaga
Melilla
Baleares
Pasajes
Marı́n y Rı́a de
Pontevedra
Santa Cruz de
Tenerife
Santander
Tarragona
Valencia
Vigo
Vilagarcı́a
0.098
0.291
0.219
0.283
0.650
0.850
0.569
0.160
0.282
0.283
0.211
0.379
0.240
0.198
0.339
0.224
0.333
0.317
0.465
0.186
0.001
0.067
0.051
0.069
0.065
0.062
0.117
0.062
0.080
0.038
0.063
0.089
0.092
0.062
0.019
0.053
0.083
0.038
0.101
0.042
0.867
0.786
0.683
0.771
0.560
0.462
0.377
0.841
0.293
0.818
0.671
0.540
0.756
0.765
0.667
0.769
0.884
0.756
0.660
0.890
0.907
0.587
0.566
0.820
0.624
0.546
0.584
0.787
0.632
1.507
0.646
0.832
0.701
0.804
0.755
0.689
2.546
0.024
0.682
0.886
0.327 0.009
0.666
0.598
0.337 0.016 0.080 0.078
0.477
0.179
0.821
0.382
0.373
0.084
0.076
0.078
0.059
0.084
0.693
0.708
0.428
0.808
0.805
0.677
0.754
0.539
0.702
0.732
0.589
0.247
0.568
0.727
0.731
Mean
Standard deviation
CV
0.348 0.063
0.217 0.050
0.619 0.791
0.690
0.241
0.350
0.462
1.090
2.357
0.455 0.064 0.321 0.105
0.247
0.040
0.202
0.057
0.543
0.630
0.630
0.543
0.099
0.098
0.050
0.067
0.089
0.494
0.492
0.249
0.336
0.446
0.136
0.057
0.131
0.167
0.168
do not cover their marginal costs. This is the case for Melilla (2.5) and Ceuta (1.5).
This result could be partially explained due to the special consideration for the legislation
of these ports. In this sense, different laws allow them special subsidies for shippers and
customers. The common characteristic for all of them is the particular location of these
ports: Ceuta and Melilla are located in cities isolated in the African continent, and both
are considered as strategic ports for the Spanish government. On the other hand, markups
for cargo (0.68) are substantially higher than that for vessels (0.46). This indicates that
shippers receive significant price concessions in relation to customers. This result would
appear to indicate the existence of fee discrimination or regulatory bias in favour of
shippers and to the detriment of freight forwarders. In the next section, we will show
whether this price discrimination can be justified by the welfare principle.
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Journal of Transport Economics and Policy
Volume 47, Part 3
Table 3 also shows the different fee elasticities which are necessary in order to calculate the superelasticities defined in Section 3 for every port authority measured on
average. All of the elasticities are negative, with values of less than one. Only one port
authority presents an own fee elasticity cargo demand higher than one, confirming the
highly inelastic nature for the demand for port infrastructure regarding the fees (Trujillo
and Nombela, 2000). In this sense, the value of the own fee elasticity of demand for
cargo is 0.45 on average, whereas the value for the own fee elasticity of demand for
vessel is 0.32. If both demands were independent, according to the inverse elasticity
rule enunciated for Ramsey, fee–cost margins for vessels should be higher than those
related to the cargo. However, cross-fee effect was statistically significant, given that the
variation on cargo fee affected the demand for port infrastructure for vessels, showing
the complementary nature of both goods. In this way the cross-fee elasticity for vessels is
0.1 on average.
6.2 Comparison fee structure with the optimal structure predicted by the model
According to equation (5), the ratio of markups should be equal to the ratio of superelasticities, which are defined as the own fee elasticity of demand minus the cross-fee
elasticity of demand. In our study, four elasticity measures are calculated: own
fee elasticities for cargo and vessels, and their corresponding cross elasticities. In order
to check whether port authorities use a second-best mechanism based on Ramsey prices,
we adopt the following strategy for the analysis: (1) we calculate the ratio of markups
and the ratio of superelasticities for each port authority during the period 1986–2005; (2)
we plot both variables in order to show the relation between them; and (3) we econometrically estimate equation (5).
In Table 4 we compare the differences between the ratio of markups based on the
estimation of the corresponding marginal costs and the ratio of superelasticities based on
the estimation of demand functions. On an aggregate level we could admit that fees
achieve the welfare maximisation condition given that the ratio of markup on average
(0.96) is equal to the ratio predicted by the Ramsey model (0.95). However, if we analyse
the mean values for the different port authorities, we observe that an important heterogeneity exists between them. In this sense, if we look at the first column, we observe that
for some port authorities the vessel fees do not cover their marginal costs, as we showed
in Section 6.1. This is the case of Ceuta and Melilla. The Ramsey pricing rule shows us
that when two products are complements, it can be the case that the price of one product
is less than its marginal cost, provided the cross-price effect is significant enough. This is
not the case of both port authorities, given that the superelasticity ratio is always
positive, so one important implication for the regulatory agency would be the revision of
current subsidies in order to make it possible for vessel fees to be able to cover the
marginal costs of port infrastructure.
In Figure 2 we plot both variables, showing that the Ramsey pricing rule is not
implemented for the case of Spanish port authorities. We observe that lower values of
the superelasticity ratio imply greater variability of the markup ratio. This is the case for
Baleares, Tenerife, Ceuta, and Melilla. This result is especially interesting given that the
first two port authorities are located on islands, whereas both Ceuta and Melilla are
cities located in Africa. Additionally, the markup ratio remains constant for those port
authorities that present a superelasticity ratio higher than approximately one.
364
Núñez-Sánchez
Marginal Costs, Price Elasticities of Demand, and Second-best Pricing
Table 4
Comparison of Markup Ratio and Superelasticity Ratio. Mean Values for Port Authorities
Port authority
Markup ratio
((PC MCC)/PC)/((PS MCS)/PS)
Superelasticity ratio
(|eSS| þ eCS)/(|eCC| þ eSC)
1.502
1.963
0.400
0.954
0.694
0.871
0.131
1.145
0.533
0.026
0.805
0.634
1.118
0.975
1.016
1.220
0.216
1.447
1.018
1.021
1.477
1.457
0.895
0.790
1.415
1.170
0.358
0.533
0.915
1.340
0.518
0.355
1.349
1.425
2.553
0.067
1.482
2.740
1.457
1.523
0.427
0.852
0.041
0.124
1.041
1.122
0.261
0.861
2.099
0.492
0.484
0.763
0.969
0.883
0.912
0.955
1.882
1.970
Bahı́a de Algeciras
Alicante
Almerı́a-Motril
Avilés
Bahı́a de Cádiz
Barcelona
Bilbao
Cartagena
Castellón
Ceuta
Ferrol-S. Cibrao
Gijón
Huelva
A Coruña
Las Palmas
Málaga
Melilla
Baleares
Pasajes
Marı́n y Rı́a de Pontevedra
Santa Cruz de Tenerife
Santander
Tarragona
Valencia
Vigo
Vilagarcı́a
Mean
Standard deviation
CV
Finally, we econometrically estimate equation (5):
2
3
ð pC MCC ð~
qÞ Þ
6
7
pC
6
7 ¼ b0 þ b1 jeSS j þ eCS þuit :
4 ð pS MCS ð~
qÞÞ 5
je j þ e
CC
pS
SC
ð14Þ
it
it
Then, we test jointly whether the coefficient related to the superelasticity ratio is one and
the constant term is zero. If we were not able to reject the null hypothesis, thus we could
admit that port authorities maximise social surplus using Ramsey prices. In Table 5 we
show that the coefficient related to the superelasticity ratio is negative (0.16), whereas
the constant term is positive (1.56). Both coefficients are statistically different from zero.
If we perform the test for both coefficients, we reject the null hypothesis of using
Ramsey pricing.
365
Volume 47, Part 3
Journal of Transport Economics and Policy
Figure 2
-10
markup ratio
10
0
20
Markup Ratio and Superelasticities Ratio
0
2
4
6
superelasticity ratio
Table 5
Parameter Estimates and Test for the Pricing Regime
constant
superelasticity
Coefficient
Std. Error
t-Statistic
Prob.
1.559
0.160
0.413
0.079
3.780
2.020
0.000
0.044
Notes: R2 ¼ 0.06, F(26,490) ¼ 9.44, Prob. > F ¼ 0.00. Joint test for constant ¼ 0 and superelasticity ¼ 1:
F(2,490) ¼ 111.49, Prob. > F ¼ 0.00.
7.0 Conclusions and Implications
From 1992 the Spanish port system has been characterised as a decentralised system
where port authorities decide their own investment and the allocation of their resources
under the self-financing principle. However, there are some aspects which port authorities cannot decide for themselves. One of them is the fee-setting mechanism, which is
regulated by the Ministry of Public Works and Transport. In Spain, port fees are
traditionally divided in two categories: those which tax general services and those which
assess specific services. From 1992, specific service fees have been decreasing in
importance. The progressive change from a tool port model, where a superstructure used
to be owned by port authorities but operated by private firms, to the landlord port
model, in which a superstructure is owned and operated by private operators, could
explain this fact. For Spanish port authorities, the two most important fees that finance
port infrastructure are those related to the movement of cargo and those that affect
366
Marginal Costs, Price Elasticities of Demand, and Second-best Pricing
Núñez-Sánchez
vessels. The centralised fee-setting mechanism is revisited, due to the claims of port authorities which highlight fees as an important strategic variable for inter-port competition.
In this paper a centralised pricing system, which allows the maximisation of social
surplus under the self-financing principle, has been presented. Moreover, both the
estimation of marginal costs of different outputs for port authorities and fee elasticities
of demand enable us to evaluate the present fee structure of port authorities.
The results obtained show that port authorities present an important degree of economies of scale and the existence of overcapitalisation, given that marginal productivity
of the quasi-fixed input is negative. Regarding individual marginal costs, differences
among different port authorities are significant. Comparing these values with their
corresponding fees, we conclude that in general terms, regulated fees for both outputs
are higher than their marginal costs, so first-best regulation is not being implemented in
the Spanish port system. However, this result seems reasonable due to the existence of
economies of scale.
On the other hand, the estimation of demand functions for the use of port infrastructure enables us to calculate fee elasticities of demand, which we consider a novelty in the
literature, given that we have not found previous studies that quantify the sensibility of
the demand for these services with regard to port fees. This analysis allows us important
conclusions. First, we have demonstrated that demands for port infrastructure are
inelastic. We have also observed the importance of time-constant effects on demand,
which could be related to the location of these infrastructures. Moreover, time effects
have been significant from 1992, so we could conclude that the decentralisation process
of port authorities has improved traffic in ports.
The comparison of fee structure with the optimal structure predicted by the model
allows us to conclude that fees do not achieve the social surplus maximisation condition.
We have also found the existence of an important heterogeneity among port authorities,
which does not enable a general recommendation regarding a new price-setting structure
for the whole of the port authorities. In this sense, a new regulation which would allow
port authorities to set their own fees may represent an improvement for the present
mechanism.
The interaction between port authority fees and cargo-handling operators’ charges
would be a good future research issue following a general equilibrium approach. However, at present this topic is beyond our scope due to the limitations of data.
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Definition
Source
infr
draft
Number of linear metres of deep water
berths of more than four metres (metres)
Total cranes (number)
Variables for the estimation of the demand functions
Qcargo Cargo (ton)
Qgt
Vessels (gross tonnage)
PC
Cargo fee (2001 constant € per ton)
PG
Vessel fee (2001 constant € per gt)
inc
Gross Domestic Product (2001 constant €)
Puertos del Estado
Puertos del Estado
Puertos del Estado
Puertos del Estado
Puertos del Estado
Instituto Nacional de
Estadı́stica (INE)
Puertos del Estado
Variables for the estimation of the cost function and expenditure functions
VC
Variable costs (2001 constant €)
Puertos del Estado
Wl
Labour price (2001 constant € per unit)
Puertos del Estado
Wk
Capital price (percentage)
Puertos del Estado, Instituto
Nacional de Estadı́stica (INE) and
Confederación Nacional de la Construcción
(SEOPAN)
Wic
Intermediate consumption price (2001
Puertos del Estado
constant hundred € per ton)
Qcargo Cargo (ton)
Puertos del Estado
Qgt
Vessels (gross tonnage)
Puertos del Estado
F
Deposit surface (squared metres)
Puertos del Estado
El
Labour expenditures (2001 constant €)
Puertos del Estado
Ek
Capital expenditures (2001 constant €)
Puertos del Estado
Eic
Intermediate consumption expenditures
Puertos del Estado
(2001 constant €)
Variable
Std. Dev.
Min.
0.195
45
8,029
56
5,010
10,801,511 10,220,888
28,978,634 38,621,171
1.342
0.729
0.237
0.150
35,519,472 29,223,918
10,801,511 10,220,888
28,978,634 38,621,171
516,580
599,368
6,637,312 4,392,354
6,651,474 5,246,096
4,175,096 3,978,286
0.334
CV
1.248 0.583
67,887,624 0.730
132,921 0.333
18.758 0.398
Max.
1
843
363 1.256
28,331 0.624
241,220 63,567,017 0.946
550,707 213,186,107 1.333
0.083
5.625 0.543
0.010
0.783 0.630
503,726 132,767,837 0.823
241,220 63,567,017 0.946
550,707 213,186,107 1.333
11,354
3,106,615 1.160
976,356 24,971,912 0.662
532,770 30,204,354 0.789
239,554 26,283,654 0.953
0.040
17,463,883 12,749,350 1,765,523
29,107
9,698
2,277
5.349
2.130
1.492
Mean
Descriptive Statistics for Variables of the Cost Function, Expenditure and Demand Functions
Appendix 1
Marginal Costs, Price Elasticities of Demand, and Second-best Pricing
Núñez-Sánchez
369